The unveiling ceremony is being held in front of the multimedia lecture hall just built in Surabaya No. 1 Middle School, the county magistrate, the leaders of the county education bureau have participated, the specifications are quite high, originally a small classroom of Surabaya No. 1 Middle School was completed and did not invite these county bigwigs to participate, the reason why they will come is because there is a person who attended, that is, the donor of the multimedia ladder classroom, the boss of Mammoth Technology, a famous mathematician in China, and the youngest professor-level researcher in China, Mr. Liu Meng.

The county magistrate shook hands with Liu Meng cordially and said sincerely: "Professor Liu, Surabaya No. 1 Middle School is very grateful for your generosity, and it is a great blessing that there are a few more talents like you in this county." ”

The director of the county education bureau and the principal and others also complimented him, and Liu Meng's head teacher also interjected and said: "When Liu Meng was different in the class, I saw that he would be extraordinary in the future, and it was so." ”

Liu Meng wanted to laugh in his heart, this class teacher is really interesting, in fact, Liu Meng was not very liked by the class teacher in the class, probably because he was too maverick, he belonged to the kind of student who had good grades but was not very obedient, and the class was the kind of teacher who was not at all immersed in reading books, and there was no sense of accomplishment as a teacher, so he definitely didn't like it so much.

The principal was obviously a little unhappy with the head teacher Li Dejin, thinking that there is no place for you to speak in this kind of scene, the two leaders haven't said a few words yet, and I haven't had time to speak, so you go up to mix, do you understand the rules, and said with a smile: "The students are looking forward to it, Mr. Liu, let's start your speech quickly." I'm going to see if I'll be able to improve even more. ”

Liu Meng nodded to a few people and walked onto the podium.

"I think many of you are probably disgusted with math. I have a headache when I see those piles of formulas, but those who really like to study mathematics usually think that mathematics is very interesting, so where is mathematics interesting and where is the beauty of mathematics? I will first use a few arithmetic problems suitable for all ages, in various forms such as theorems, interesting problems and even unsolved puzzles, to lead you to peek into a corner of the mathematical world. Many of the problems contain profound mathematical knowledge behind them, touching on all areas of mathematics. I hope that students who have failed mathematics since childhood will enjoy the fun subject of mathematics. ”

"The first small problem, the digital black hole 6174. Pick any four-digit number, of course, the numbers can't be all the same, and arrange all the numbers from highest to smallest. Then arrange all the numbers from the smallest to the largest, and subtract the smaller number of the former from the smaller number of the latter to get a new number. Repeat the above operation for the newly obtained number, and you will inevitably get 6174 within 7 steps. Isn't that interesting? That might not be intuitive, okay. Let me give you an example. For example, select four digits 6767: 7766-6677=1089;9810-0189=9621;9621-1269=8352;8532-2358=6174;7641-1467=6174...... The 'black hole' of 6174 is called the Kaprekar constant. For three-digit numbers, there is also a number black hole 495. In fact, starting from this question, we can also ask a question, that is, in addition to three-digit and four-digit numbers, there are digital black holes, so are there five-digit, six-digit, and seven-digit numbers?

After the first small question was finished, everyone present was attracted by Liu Meng's speech. This knowledge is not something that high school teachers can tell, in fact, the teachers of Surabaya No. 1 High School are roughly divided into two categories. The first is to graduate from high school or junior college in the early years to teach in the school, but the number of years of teaching is also established, but the teaching level can be imagined, experienced, but the vision is far from enough, the second is the young teacher who has just graduated from the ordinary undergraduate, these teachers themselves are almost all the kind of students who study hard but the grades are not very good when they are in high school, and even some repeat a few years before being admitted to the most general undergraduate, and after four years in the school, he became a high school teacher, at such a level, how high can you expect his teaching level to beJust follow the script.

Liu Meng remembers very clearly, the English teacher, math teacher, Biology teachers belong to the first situation, physics teachers belong to the second situation, among which the physics teacher is the most engaged, the young man who has just graduated is still tender, the class is to read the book, many times on the blackboard to check the problem is often wrong, provoked the following classmates boo, this young man is also persistent, he stands aside and watches, usually can find out where he is wrong, such a teacher, inexperienced, poor talent, what kind of good students can be taught? Therefore, all the students in Liu Meng's class at that time who had better grades relied on self-study, and the students who listened carefully to the teacher's class were only the kind with very average grades.

After listening to the first question, the students discussed it loudly, and all of a sudden they all felt that mathematics was really fun, and Liu Meng waited for a while before starting to talk about the second question.

"The second is the 3x+1 problem, starting with any positive integer and repeating it by dividing it by 2 if it is even, and expanding it by 3 times and adding 1 if it is odd. You will find that the sequence will always end up being 4, 2, 1, 4, 2, 1,... of the cycle. For example, if the selected number is 67, we can get it according to the above rules: 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 1, 4, 2, 1...... Mathematicians tried many numbers, but none of them escaped the '421 trap'. But is it true that for all numbers, the sequence will always end up in a 4,2,1 cycle?"

There was a lot of discussion among the students, and some of them have even begun to try to calculate it.

Liu Meng continued: "This question can be described as a huge hole - at first glance, the problem is very simple. There are many breakthroughs, so many mathematicians jump into them, but they don't know that it is easy to get in and difficult to get out, and many mathematicians have not solved this problem until they die. There are countless mathematicians who have already been recruited. This can be seen in the various aliases of 3x+1 problems: 3x+1 problems are also called Collatz conjectures, Syracuse problems, Kakutani problems, Hasse algorithms, Ulam problems, and so on. Later, due to the controversy over the naming, it was simply left alone and simply called the 3x+1 problem. ”

"In number theory, as long as the seemingly simple propositions generalized to infinite numbers are very difficult to prove, because you can't always prove them one by one, such as the famous Riemann conjecture, Fermat's theorem, and Goldbach's conjecture. The same is true for the 3x+1 problem, which until now has not been proven by mathematicians. This law holds true for all numbers. If anyone can prove this problem, he will be one of the greatest mathematicians, at least one of the top ten most famous people on this planet. At least it is much more powerful than the well-known Chen Jingrun and Hua Luogeng. ”

The students were immediately fried into a pot of porridge. For high school students, especially those in a remote town, it is simply opening up another world, and the blood is surging, and the students who usually claim to be smarter can't wait to take out a paper and pen to check it, fantasizing that they can solve the problem and become famous. He was admitted to Mizuki University and Yenching University...... And so on, young people are always impulsive and naïve and full of fantasies.

Liu Meng's speech was extremely simple for these students. The students who are sitting in the math are very bad and have failed can easily understand these problems, but they are very different, the impact on them can be imagined, this effect Liu Meng is very satisfied, but also has some ideas, in fact, the younger the contact with these world problems, the greater the chance of solving them, just like Wiles is in childhood contact with Fermat's theorem, Mr. Kong came into contact with Goldbach's conjecture is already high school, it is a little late, in childhood there are thoughts, and when the university is finished with means, it is very likely to have new ideas, it is very likely to achieve great achievements, but today's Chinese teaching is at the beginningIn high school, I learned too much difficult and uninnovative knowledge, students are always doing questions over and over again, and even some so-called well-known high schools have exams every week, and even have to make up classes on weekends, the so-called admission rate is really blinding, but what will these depressed high school students do after entering college?

The suppressed youth hormones have exploded, and those missed TV series, movies, and games have to be made up, and the curiosity and restlessness about the opposite sex have also to explode, and when they enter the college campus, it is almost the spring zoo, just like what Mr. Zhao said, "Spring is here, and the season for animals to courtship and mate ......"

More than 90% of college students talk about women all day long, and a few are interested in scientific issues, which is the biggest drawback of Chinese teaching, whether parents and teachers always like to instill knowledge into children's minds in advance, so what is the use? Relatively speaking, Liu Meng is more admiring the American teaching method, that is, to let students who are really interested in learning more deeply, maybe most people are very misunderstood, thinking that American high school mathematics, physics, Chemistry and so on are too simple, this is wrong, the basic teaching of high school in the United States is indeed very simple, but students can take difficult courses by themselves, for example, if you dare to be interested in mathematics, you can take advanced courses in mathematics, these advanced courses are the advanced mathematics of the first year of Huaxia, and the same is true for other subjects, which is to let the students who dare to be interested learn more deeply.

Instead of the teaching method of Huaxia, everyone earnestly studies the periodic table, all kinds of complex chemical reactions, complex organic structures, complex mechanical formulas, complex conservation of momentum, and complex mathematical knowledge, but how many people are really interested? How many people will really use this knowledge in the next ten years? How many people will return all the things they have learned to cope with the exam to the teacher within a few years of graduation? It should be the vast majority of people! This is a waste of the intelligence of young people in the whole society, which is more poisonous than the imperial examination of Baguwen, and it is very unscientific, and it hinders the progress of society.

Liu Meng suddenly felt that this speech was very meaningful, opening up the limited sky for young people. These small math problems can be understood even by junior high school students, and the enlightenment should be earlier, thinking of this, I have some thoughts and continues: "The next small problem is the quick calculation of special two-digit multiplication. If the tens of two two-digit numbers are the same, and the single digits add up to 10, then you can immediately say the product of these two numbers. If these two numbers are written as AB and AC respectively, then the first two digits of their products are the product of A and A+1, and the last two digits are the product of B and C. For example, 47 and 43 have the same number of tens, and the sum of the single digits is 10. Thus the first two digits of their product are 4× (4+1)=20, and the last two digits are 7×3=21. That is, 47×43=2021. Similarly. 61×69=4209, 86×84=7224, 35×35=1225, etc. So why on earth?" Liu Meng said and asked the question with a smile.

The students immediately thought about it. After a while, a very thin classmate in the front row raised his hand and said, "I know." ”

Liu Meng was very happy. Signaling him to say it, the student was very excited, stood up and said: "The reason behind this quick calculation method is that such two digits can represent bits (10x+y) and (10x+(10-y)), and multiplying them is 100x(x+1)+y(10-y), which is true for any x and y, so it can be calculated so quickly." ”

Liu Meng exclaimed: "That's true, it seems that this classmate is very interested in mathematics." You might as well listen to some teachers' lectures, and after learning the content of high school, you can study some difficult and innovative mathematical propositions. The achievements are certainly not small. ”

With Liu Meng's approval, these classmates were very excited, their chests were heaving, and their faces were very proud and proud. Who is Liu Meng? That is the most famous mathematician in China today, and there is no one who even surpasses other well-known mathematicians in China in the past, and what a high honor it is to be praised by him? It is no wonder that this student is so excited.

"Magic square, everyone should have played it, a third-order magic square is to fill in the numbers 1 to 9 into a square of 3×3, so that the sum of the three numbers in each row, column and two diagonals is exactly the same. For example, the first row 8, 1, 6, the second row 3, 5, 7, the third row 4, 9, 2, the sum of the three numbers on each line is equal to 15. You may have heard of the Magic Square, but you may not know some of the wonderful properties in the Magic Square. For example, if any third-order magic square satisfies the sum of the squares of the three digits in each row is equal to the sum of the squares of the three digits in reverse order. For the third-order magic square just mentioned, it is satisfied, the sum of the squares of 816, 357, and 492 is equal to the sum of the squares of 618, 753, and 294, as for why there is such a property? ”

Liu Meng's small mathematical problems today really hooked everyone's interest, the most important thing is that they are simple problems, but after Liu Meng's words, suddenly it became high-end, and he became the most awesome mathematician to solve such a simple problem, more awesome than those students who won the gold medal in Olympiad, and a new broad road appeared in front of them, so that these people are studying, reviewing, exams, and so on all day long. In the boredom and depression of make-up classes, waiting for the arrival of the college entrance examination, students who hope to be admitted to a key university have a feeling of being sudden.

"The 196 algorithm, a number is read forward and backward is the same, so we call it palindrome number. Take a random number and add it backwards until you get a palindrome number. For example, if the selected number is 67, you can get a palindrome number 484 in two steps: 67 + 76 = 143, 143 + 341 = 484, and it takes four steps to turn 69 into a palindrome number: 69 + 96 = 165, 165 + 561 = 726, 726 + 627 = 1353, 1353 + 3531 = 4884, and the road to the palindrome number of 89 is particularly long, and the first palindromic number will not be obtained until step 24, 8813200023188. ”

"It's not surprising that students may think that they will always end up with a palindrome number by adding up one plus one against each other. This is also true - for almost all numbers, the rules are kept on and on. Sooner or later, there will be a palindrome number. However, 196 is a rather striking exception. Mathematicians have calculated more than 300 million digits with computers, and none of them have produced a single palindrome number. Departure from 196. Is it possible to add palindromes? What is so special about 196? This is still a mystery, and if any of you can solve this mystery, maybe a new branch of number theory can be opened. ”

Liu Meng threw out a few seemingly simple and unsolved problems have made the students unavoidable, Liu Meng is well aware of these high school children, think that the teacher said when talking about the structure of the benzene ring that if any student can solve a similar problem can win the Nobel Prize, the students were so excited after listening to it, and now Liu Meng is now simple and so specific. And the unsolved problems are thrown to the students, and the result can be imagined, the whole process. The students are all enthusiastic, and they can't wait to solve one of the problems Liu Meng said immediately, or solve all of them.

The only solution

"Classic number puzzle: use 1 to 9 to form a nine-digit number so that the first digit of the number is divisible by 1. The first two digits are divisible by 2. The first three digits are divisible by 3, and so on, until the entire nine-digit number is divisible by 9. You heard it right, there really is such a huge number: 381654729. where 3 is divisible by 1, 38 divisible by 2, 381 divisible by 3, and the whole number divisible by 9. This number can be derived step by step using the property of divisibility or can be found using computer programming. Another interesting fact is. Of all the 362,880 different nine-digit numbers made up of 1 to 9, 381654729 is the only one that satisfies the requirements!"

"The numbers are changing. The number remains the same, twice as many as the 123456789 is 246913578, which is exactly another number made up of 1 to 9. Twice as many as 246913578 is 493827156, which is exactly another number made up of 1 to 9. Doubling the 493827156 again, 987654312, it still happens to be made up of numbers 1 to 9. If you double the 987654312 again, you will get a 10-digit 1975308624 that still has no repeat numbers in it, and it happens to be made up of 10 numbers from 0 to 9. Double the 1975308624 again, and the number will become 3950617248, which is still made up of 0 to 9. So, will this rule continue forever? Let's wait for the students to check it themselves. ”

Liu Meng talked about several interesting small problems in number theory in a row, and the students in the audience were full of interest, not only that, but even the county magistrate, the county education director, the senior and many teachers sitting below listened attentively, and some teachers who taught mathematics couldn't help but check it according to Liu Meng's ideas, and the county magistrate sighed: " You all listen, the master is different, we all understand that we can say such a profound problem in simple terms, your teacher should teach like this, sometimes my son's homework is brought back, only junior high school, I sometimes can't understand, this is the gap, stupid people always like to complicate simple problems to show that they are not stupid enough, confident genius is to simplify the most complex problems so that everyone understands. ”

The director of the education bureau, the principal and the teachers nodded their heads in agreement, "What the county magistrate said is that our education work must be improved." "That being said, who knows if these guys are going to improve or not?

Liu Meng then elaborated on Goldbach's conjecture in simple terms, this is an authentic world-class problem, Liu Meng is a little bit away from solving her but suddenly stuck for more than a year, this year he tried all kinds of experiences can not solve, can only give up and return to his hometown, and turn to carry out the education work in his hometown, in fact, he hopes to find inspiration from the thinking of these students, young people's ideas are wild, and it is possible to open up their minds again, those famous mathematicians have already been eroded by too many mindsets.

"If any of you have any ideas about Goldbach's conjecture, you can come to me, and I'll be at Mammoth Tech next door for the next week, even if it's unrealistic, you can come to me boldly, dare to think first. Liu Meng said with a smile.

The students were in an uproar and immediately began to think hard, and Liu Meng added: "If any student's ideas inspire me and I really love mathematics, I can recommend them to Mizuki University to participate in early admission." ”

You must know that the teaching level of Surabaya No. 1 Middle School is not high, especially the English teaching faculty is too poor, no one has been able to be admitted to Shuimu University for three consecutive years, and it is a very glorious thing to be admitted to Shuimu University in Surabaya City, and the whole county will go crazy, especially with face.

Liu Meng's words are definitely not bragging, since he published a paper on twin primes, plus the professor-level researcher who was hired to solve the Sitapan conjecture before, and now he is the first mathematician in Huaxia, after his return, Shuimu University has sent him an invitation letter, hired as a professor of Shuimu University, and the treatment given is more generous, Liu Meng did not directly agree, Shuimu University invited him to be a judge of what award, according to the people who contacted him, this scholarship is the most valuable award of Shuimu University, each student can only participate in the evaluation once during the university, and there are only ten undergraduates a yearIf Mizuki University is a holy place in the hearts of all Chinese students and think about it, then this award is a holy place in the hearts of all Mizuki University students and haunted by dreams, its high force can be imagined, Liu Meng has agreed to be a judge, just two weeks later.

Liu Meng continued: " In fact, to engage in mathematics, thinking is the most important, the so-called thinking is the illusory point of the soul is the shining point in the depths of the soul, simply put, the angle of cutting into the problem should be different, Gauss's story students must know, the teacher assigned a problem, 1 to 100 add up, all the students use this method to add, but he thought of using the number series to solve, even if the mental arithmetic is not as good as Gauss's unique thinking to get the answer fast, this is the power of thinking, so thinking is a force that is stronger than ability and knowledge。 ”

"So the most important thing in this talk, at the end, tell a little story, to see which student can get the answer the fastest, two trains are 200 kilometers apart, each traveling in the opposite direction at a speed of 50 kilometers per hour. A fly flies back and forth between the two trains at a speed of 75 kilometers per hour from the front of one of the trains, and the question is: What is the total distance the fly flies until the two trains collide?

Liu Meng's question came out, everyone took out a pen and paper to calculate, although Liu Meng just said that thinking is the most important, but in the case of time constraints, students are still used to starting to calculate, this is the influence of the mindset, in fact, this question is like 1+2+3 has been added to 100 questions, it is very easy to find the right entry point. (To be continued......)